Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

2.4 Kinetics of second-order reactions 24
2.4 Kinetics of second-order reactions
2.4.1 A + A → products
A+A→ P (2.79)
I
Solution of the rate equation:
Integration:
y
Initial value condition at =0:
− 1 [A]
= [A] 2 (2.80)
2
[A]
2
= −2 (2.81)
[A]
− 1 = −2 + (2.82)
[A]
[A ( =0)]=[A] 0
(2.83)
y
Solution for [A ()] (Fig. 2.15):
= − 1
[A] 0
(2.84)
1
[A] = 1 +2 (2.85)
[A] 0
I Experimental determination of k:
(1) Graphical method:
1
[A] = 1
[A] 0
+2 (2.86)
⇒ Plot of [A] −1 vs. gives a straight line with slope =2 (Fig. 2.9).
⇒ We do need to know the absolute concentration of [A]!
(2) We can again use a nonlinear least squares fitting method (Appendix B).